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We study the efficacy and efficiency of deep generative networks for approximating probability distributions.
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Covering a ball with smaller equal balls in 𝐑 n \mathbf{R}^{n}
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Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements
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Foundations of quantization for probability distributions
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Optimal transport: old and new , volume 338
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Rectified linear units improve restricted boltzmann machines
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Hilbert space embeddings and metrics on probability measures
Bharath K Sriperumbudur, Arthur Gretton, Kenji Fukumizu, Bernhard Schölkopf, and Gert RG Lanckriet · 2010
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Reproducing kernel Hilbert spaces in probability and statistics
Alain Berlinet and Christine Thomas-Agnan · 2011
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A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2014
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Training generative neural networks via maximum mean discrepancy optimization
Gintare Karolina Dziugaite, Daniel M Roy, and Zoubin Ghahramani · 2015
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Measure theory and fine properties of functions
Lawrence Craig Evans and Ronald F Gariepy · 2015
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How well generative adversarial networks learn distributions
Tengyuan Liang · 2018
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Foundations of machine learning
Mehryar Mohri, Afshin Rostamizadeh, and Ameet Talwalkar · 2018
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Optimal approximation of piecewise smooth functions using deep relu neural networks
Philipp Petersen and Felix Voigtlaender · 2018
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Optimal approximation of continuous functions by very deep relu networks
Dmitry Yarotsky · 2018
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One-dimensional empirical measures, order statistics, and Kantorovich transport distances , volume 261
Sergey Bobkov and Michel Ledoux · 2019
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Sharp asymptotic and finite-sample rates of convergence of empirical measures in wasserstein distance
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On the rate of convergence in wasserstein distance of the empirical measure
Nicolas Fournier and Arnaud Guillin · 2015
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Generative moment matching networks
Yujia Li, Kevin Swersky, and Rich Zemel · 2015
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Generating sentences from a continuous space
Samuel R Bowman, Luke Vilnis, Oriol Vinyals, Andrew M Dai, Rafal Jozefowicz, and Samy Bengio · 2016
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Image style transfer using convolutional neural networks
Leon A Gatys, Alexander S Ecker, and Matthias Bethge · 2016
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f-gan: Training generative neural samplers using variational divergence minimization
Sebastian Nowozin, Botond Cseke, and Ryota Tomioka · 2016
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Generative adversarial text to image synthesis
Scott Reed, Zeynep Akata, Xinchen Yan, Lajanugen Logeswaran, Bernt Schiele, and Honglak Lee · 2016
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Jonathan Weed and Francis Bach · 2019
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Estimation of smooth densities in wasserstein distance
Jonathan Weed and Quentin Berthet · 2019
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Generative adversarial network in medical imaging: A review
Xin Yi, Ekta Walia, and Paul Babyn · 2019
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Statistical guarantees of generative adversarial networks for distribution estimation
Minshuo Chen, Wenjing Liao, Hongyuan Zha, and Tuo Zhao · 2020
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Convergence and concentration of empirical measures under wasserstein distance in unbounded functional spaces
Jing Lei · 2020
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Deep network approximation for smooth functions
Jianfeng Lu, Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
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A universal approximation theorem of deep neural networks for expressing probability distributions
Yulong Lu and Jianfeng Lu · 2020
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Constructive universal high-dimensional distribution generation through deep relu networks
Dmytro Perekrestenko, Stephan Müller, and Helmut Bölcskei · 2020
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Deep network approximation characterized by number of neurons
Zuowei Shen, Haizhao Yang, and Shijun Zhang · 2020
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The phase diagram of approximation rates for deep neural networks
Dmitry Yarotsky and Anton Zhevnerchuk · 2020
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Nonlinear approximation and (deep) relu networks
Ingrid Daubechies, Ronald DeVore, Simon Foucart, Boris Hanin, and Guergana Petrova · 2021
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High-dimensional distribution generation through deep neural networks
Dmytro Perekrestenko, Léandre Eberhard, and Helmut Bölcskei · 2021
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